2018 Volume 59 Issue 1 Pages 47-52
Characteristic property changes were observed for high density and high purity nanocrystalline (n-) Au prepared by the gas deposition method. The increase in internal friction with a modulus defect started at ～180 K and became steep above 200 K. An increase in endothermic heat flow began at ～170 K. The electrical resistivity showed a deviation from a linear increase with the temperature at ～130 K. All the characteristic changes were reproduced by the repetition of the thermal cycle below 300 K, but the amounts diminished after the grain growth. These characteristic temperature changes indicate a glass-transition-like behavior of the grain boundaries in n-Au.
Nanocrystalline (n-) materials have attracted attention because of their unique structure, in which ultrafine crystallites with a grain size of less than 100 nm are surrounded by disordered grain boundaries. For metallic materials with ultrafine polycrystalline states, the most prominent and technologically important feature is the increase in strength with decreasing grain size (Hall-Petch effect). A strength and hardness much higher than those of the conventional polycrystalline (p-) counterparts were reported for n-metals1–3). However, the increase in strength of n-metals showed saturation and decreased with the further decrease in grain size to less than ～20 nm (inverse Hall-Petch effect)4,5). The inverse Hall-Petch effect was attributed to sliding or shear deformation at the grain boundaries6,7). The increased volume fraction of the grain boundaries also affected other physical properties of n-metals; for example, higher electrical resistivity than that of p-metals was reported8,9). These observations suggest that the behavior of the grain boundaries play an important role on the characteristic properties of n-metals.
For p-metals, the positions of atoms at the grain boundaries are not random like they are in amorphous solids; further, periodic arrangements of structural units with atoms were observed for the grain boundaries of p-metals via scanning transmission electron microscopy10,11). From the molecular dynamics simulation, on the other hand, dynamic behavior similar to that of glass-forming liquids was suggested for the grain boundaries of p-materials at high temperatures12). Furthermore, first-order transition of order-disorder in the grain boundaries below the melting point13) and reversible structural transformation in Cu ∑5(310) grain boundaries14) have also been observed. Moreover, the liquid-like state of grain boundaries was identified using molecular dynamics simulations of n-Si and n-metals15–17). For colloidal crystals with a diameter of 600 nm, the glass transition of grain boundaries was recently suggested from confocal optical microscope observations18). However, no experimental results have been reported to support the amorphous state or glass-like characteristics of the grain boundaries in metals.
For n-Au in the as-prepared state, we reported that the internal friction showed an anomalous large increase above 200 K ($Q_{ > 200K}^{ - 1}$, see Fig. 2)19). It was found that $Q_{ > 200K}^{ - 1}$ was repeatedly observed for cooling and warming below 350 K but the amount decreased with grain growth after heating above 350 K. These observations suggested that some anelastic process of grain boundaries was thermally activated above ～200 K in n-Au20). The internal friction due to grain boundaries was observed in p-Au also but at much higher temperatures above ～400 K at a similar measurement frequency21). In our previous thermal analysis, an endothermic tendency of n-Au compared with p-Au was observed above ～200 K22). The endothermic tendency disappeared after grain growth by annealing above 350 K. Further, the strongly preferred orientation of the crystallites in n-Au turned to random orientations but no grain growth was observed after plastic creep deformation at room temperature23). On the other hand, it was suggested that the plastic creep deformation of n-Au at liquid nitrogen temperature was governed by dislocation motions or twin formation22). These results indicate that the grain boundaries of n-Au become anelastic or viscoelastic above ～200 K, like metallic glasses above the glass transition temperature; the viscoelasticity of the grain boundaries aids plastic deformation by grain sliding with the rotation of the crystallites. The viscoelastic state appears to be quasi-stable because no grain growth occurs during the plastic deformation.
If $Q_{ > 200K}^{ - 1}$ reflects a state change of the grain boundaries from ideal elastic to anelastic or viscoelastic, corresponding variations are expected for other physical properties. In the present study, possible changes in thermal properties and electrical resistivity of n-Au were carefully measured at low temperatures, and the results were compared with those of anelasticity in order to survey the amorphous behavior of the grain boundaries.
Nanocrystalline Au specimens were prepared by the gas deposition (GD) method19). In this method, ultrafine Au particles formed by the gas condensation process were directly deposited on a cooled glass substrate by using a He gas jet flow. The purity of He was maintained above 99.9999% by a purification system in order to obtain contamination-free and fully dense specimens. Ribbon-like specimens with a length, width, and thickness of ～23 mm, 1 mm, and 0.05 mm, respectively, were deposited on the glass substrate. The substrate was cooled by a cold finger connected to a liquid nitrogen reservoir. The deposition rate (deposited thickness per unit area and unit time) was controlled by the crucible temperature for the nanoparticle preparation by the gas condensation method. The crucible temperature was measured by using a pyrometer and the substrate temperature was measured by using a thermocouple. The deposition rate, crucible temperature, and substrate temperature are listed in Table 1. The deposited ribbons were carefully removed from the substrate. After the preparation, all n-Au specimens were stored in a refrigerator at 260 K.
| Specimen | A | B | C |
|---|---|---|---|
| Depo. rate [nm/s] | 202 | 161 | 112 |
| Crucible temp. [K] | 1882 | 1807 | 1726 |
| Substrate temp. [K] | 255 | 256 | 256 |
| Lattice parameter [Å] |
4.0732 ± 0.0008 | 4.0783 ± 0.0008 | 4.0794 ± 0.0008 |
| Mean grain size [nm] |
28 ± 2 | 31 ± 1 | 40 ± 2 |
| Microstrain [%] | 0.1 ± 0.01 | 0.09 ± 0.01 | 0.07 ± 0.01 |
| Relative density | 0.98 ± 0.01 | 1.00 ± 0.01 | 1.01 ± 0.01 |
The density of the specimens was evaluated using the Archimedes method with high-purity ethanol. The lattice parameter and mean grain size were determined by X-ray diffraction measurements with Cu-Kα radiation (X'Pert PRO, PANalytical, 45 kV and 40 mA). Nelson-Riley analysis24) was applied for diffraction peaks to evaluate the lattice parameter. The mean grain size and microstrain were evaluated from the broadening of diffraction peaks by using Halder-Wagner plots25). The internal friction and resonant frequency were measured by using the electrostatically excited flexural resonant vibration of a reed specimen (resonant frequency ～650 Hz)19).
Differential scanning calorimetry (DSC) was conducted on an X-DSC7000 (Seiko Instruments Inc.) for a specimen of ～5 mg at a heating rate of 20 K/min in the temperature range between 140 and 300 K. The electrical resistivity was measured by the four-probe method in the temperature range between 80 and 300 K.
The mean grain size, microstrain, lattice parameter, and density of n-Au prepared and used in the present study are listed in Table 1. In the as-prepared state, the mean grain size of n-Au used ranged from 28 to 40 nm and the density was more than 98% of that of p-Au. The lattice parameters of specimens B and C in the as-prepared state were identical to those of p-Au (a0 = 4.07865 nm) within the present experimental error. However, the lattice parameters of specimen A were smaller than those of p-Au and the normalized change (Δa/a0 = (a − a0)/a0, a0 is the lattice parameter of p-Au) of specimen A was Δa/a0 = −0.13%. For comparison, Δa/a0 = −0.006% was reported for IGCC n-Pd26) with the grain size of 40 nm. A maximum lattice contraction of Δa/a0 = −0.01% was also reported for BM n-Ni, n-Cu27), and n-W28). Our previous study suggested that the lattice parameters of n-Au were smaller than those of p-Au by ～0.05% and the vacancy concentration was ～0.1% in the as-prepared state29).
Figure 1 shows the XRD patterns of specimens A, B and C. All specimens show a strong (111) preferred orientation in which the (111) planes of most crystallites are parallel to the specimen surface in the as-prepared state. The (111) preferred orientation of specimen A was changed to the (100) preferred one by the grain growth after heat treatment to 660 K. Grain growth and weakening in the (111) preferred orientation were observed for specimen B after aging at 260 K for 18 months or after heat treatment to 723 K. There were several reports that the grain growth was enhanced in n-metals. Grain growth of n-Cu was reported during the indentation test at 83 K30). The grain growth of n-Ni during deformation was reported even at an applied stress as low as 20% of its yield stress31). Without the applied stress, the grain size of n-Pd increased from 10 to 45 nm when kept at room temperature for 20 h32,33). For GD n-Au, no obvious grain growth was observed after plastic deformation at room temperature23) or storage at room temperature for several days.
X-ray diffraction patterns of n-Au used for (a) internal friction (specimen A), (b) differential scanning calorimetry (specimen B), and (c) electrical resistivity (specimen C) measurements. In (a) and (b), the patterns after warm-up to elevated temperatures and aging at 260 K for 18 months are also shown.
Figure 2 shows the temperature changes in the resonant frequency (f) and internal friction (Q−1) of n-Au (specimen A). As reported by our previous study19), a rapid increase in Q−1 was observed above ～200 K ($Q_{ > 200K}^{ - 1}$) in the as-prepared state. In Fig. 2(a), careful observation indicates that the increase in Q−1 started below ～200 K. Corresponding to $Q_{ > 200K}^{ - 1}$, the resonant frequency showed a rapider decrease as the temperature increases above ～200 K. The same temperature dependences in f and Q−1 were observed for the repetition of the measurements from 30 to 300 K. Since $Q_{ > 200K}^{ - 1}$ became small with the grain growth induced by annealing above 350 K, $Q_{ > 200K}^{ - 1}$ was attributed to an anelastic process activated in the grain boundaries above ～200 K29,34). It is noted that $Q_{ > 200K}^{ - 1}$ was commonly reported for other FCC n-metals such as n-Cu34), n-Al35), and n-Ag36). The sliding motions of grain boundaries in p-metals were intensively investigated by anelasticity measurements37). The atomistic process of grain boundary anelasticity was investigated from the experiments using bi-crystals and molecular dynamics simulations38,39). Migration of the grain boundaries perpendicular to the boundary plane was attributed to the origin of grain boundary anelasticity at lower temperature, and the sliding motion along the boundary plane was to the origin of anelasticity at higher temperature.
Temperature induced changes in resonant frequency (f, 2Δf/f～ΔE/E, where E is the dynamic Young's modulus) and internal friction (Q−1) observed for n-Au (specimen A) in the as-prepared state (solid line) and after heating to 400 K (dotted and dashed line) and 500 K (dashed line).
In the resonant vibration measurement, the increase in f reflects the increase in the dynamic modulus. The dynamic modulus of anelastic materials normally shows an increase with the decrease of the anelastic strain. In Fig. 1, Q−1 was decreased but f showed a decrease by the grain growth after warm-up. As shown in Fig. 1(a), the (111) preferred orientation in the as-prepared state was changed to the (100) preferred one by the grain growth after thermal treatment to 660 K. The value of dynamic Young's modulus of Au much depends on the crystallographic directions, and those along the <111>, <110>, and <100> directions are 116, 81.3, and 41.3 GPa at 300 K, respectively40). The decrease in f by the grain growth in Fig. 2(a) mainly reflects the texture change by the grain growth as the mean dynamic modulus along the specimen length direction became lower.
For plastically deformed FCC p-metals, a relaxation peak with the modulus defect was observed (Bordoni peak) and explained by the kink-pair formation process of dislocations41). The Bordoni peak of p-Au was observed at ～110 K under the measurement frequency at ～650 Hz. The dislocation activity in n-metals is still an open question and the mechanism for the Q−1 peak at ～100 K displayed in Fig. 1 is outside the scope of the present study.
3.3 Thermal propertiesAs mentioned in section 3.2, the observation of $Q_{ > 200K}^{ - 1}$ indicates that certain atomic motions are thermally activated in the grain boundaries above ～200 K. Our previous and preliminary thermal measurements suggested that the heat capacity increased above ～200 K22). Figure 3(a) shows the results of differential scanning calorimetry (DSC) measurements during heating from 140 to 300 K, where the heat flow curves of n-Au (specimen B) in the as-prepared state and n-Au after heating to 723 K are depicted. The heat flow of n-Au in the as-prepared state became endothermic above ～170 K compared with that of n-Au after heating to 723 K. It is noted that the heat flow curve was reproduced within the variation shown in Fig. 3(a) for the repetition of the thermal measurements from 140 to 300 K. The deviation in the endothermic heat flow of n-Au after heating to 723 K is plotted in Fig. 3(b). An endothermic tendency above ～170 K was clearly seen for n-Au in the as-prepared state. It is known that thermally stable amorphous alloys known as metallic glasses, showed a step-like increase in heat capacity42) and a rapid increase in anelasticity43) at the glass transition temperature during heating. In Fig. 3, the result of specimen B stored at 260 K for 18 months is also shown. The endothermic tendency was similar to that in the as-prepared state, but the onset temperature shifted slightly to a higher temperature. The grain growth from 31 to 67 nm was found by the aging at 260 K. At the same time, the internal friction shows a slight decrease (see Fig. 5(a)); however, $Q_{ > 200K}^{ - 1}$ remained similar to that observed in the as-prepared state. These observations suggest that the amount of grain boundaries decreased but the nature of the grain boundaries was not greatly modified by the aging at 260 K.
(a) Heat flow curves measured for n-Au (specimen B) in the as-prepare state (solid line), stored at 260 K for 18 months (dotted and dashed line), after heating to 723 K (p-Au, dashed line) measured by differential scanning calorimetry. The smaller bar indicates the maximum variation in the heat flow curve, where the measurement during heating from 140 to 300 K was repeated. (b) Subtracted endothermic heat flow curves for n-Au in the as-prepare state and aged at 260 K, where the heat flow of n-Au after heating to 723 K was used as a reference.
The temperature change in electrical resistivity of n-Au (specimens B and C) in the as-prepared state is depicted in Fig. 4. The same temperature dependence is observed for the repetition of the cool-down and warm-up procedure below room temperature. The electrical resistivity of n-Au in the as-prepared state is higher than that of p-Au for the temperature range investigated. In the range between 90 and 300 K, the electrical resistivity of p-Au increases linearly with the temperature. Above ～130 K, the electrical resistivity of both specimens B and C show a slight downward deviation from a linear increase with increasing temperature. The deviations in the resistivity from the linear extrapolation for the observed data below 120 K (dashed lines in Fig. 4(a)) are shown in Fig. 4(b). The magnitude of the deviation is not the same but the behavior is quite similar for both the specimens. The temperature dependence of the resistivity of GD n-Au was reported by Ederth et al. and a discontinuous change in electrical resistivity below 10 K was discussed44). A similar deviation from the linear temperature increase above ～150 K was observed for Ederth' data by carefully monitoring the temperature dependence.
(a) Temperature dependence of electrical resistivity of n-Au (specimens B (black) and C (gray)) in the as-prepared state. The dashed lines indicate the linear extrapolations for the observed data below 120 K. The data reported for p-Au is also shown. (b) Deviation in electrical resistivity from the linear dashed line determined by the extrapolation from the data below 120 K.
The electrical resistivity of specimen C was higher than that of specimen B. The mean grain size of specimen C was somewhat larger than that of specimen B. In Table 1, the deposition rate of specimen C is about 30% smaller than that of specimen B. We reported that the texture and property of n-Au prepared at the higher deposition rate were different from those at the lower rate23,29). The resistivity of specimen C higher than that of specimen B indicates the difference in the grain boundary state between them; however, the details of the relationship between the grain boundary state and resistivity are still unclarified at present.
Characteristic changes in anelastic, thermal, and electrical properties were found above ～130 K as shown in Figs. 2, 3, and 4, respectively. These characteristic changes were similarly observed for the repetition of the cool-down and warm-up procedure below room temperature. However, the proportion of the characteristic changes decreased with the grain growth. These results are summarized in Fig. 5. The DSC measurements clearly indicated that the endothermic tendency or the increase in specific heat began at ～170 K in the as-prepared state. The careful observation of the internal friction spectrum also revealed that the increase started above ～180 K.
Characteristic temperature-dependent changes in physical properties of n-Au in the as-prepare state and aged at 260 K. (a) Internal friction spectra of n-Au (specimen A) in the as-prepared state (solid line) and after aging at 260 K for 12 months (dotted and dashed line). (b) Deviation in endothermic heat flow from that of p-Au (specimen B, identical to Fig. 3(b)). The right-hand-side axis indicates the conversion to the deviation in heat capacity. (c) Deviation in electrical resistivity from the linear temperature change estimated from the extrapolation for the observed data below 120 K observed for n-Au (specimens B and C) in the as-prepared state (identical to Fig. 4(b)).
As already mentioned, the metallic glasses showed a step-like increase in the specific heat42) and a rapid increase in anelasticity43) at the glass transition temperature, where amorphous materials transform from an elastic solid to a supercooled viscoelastic liquid state. It was reported that the electrical resistivity of the metallic glasses decreased upon heating (negative Temperature Coefficient of Resistivity (TCR)) and the TCR became more negative at glass transition temperature42,45). The negative TCR below the glass transition was qualitatively explained by the variation in the structure factor of Ziman's model for pure liquid metals, and the configurational changes as well as the phonon properties for the more negative values around the glass transition.
As shown in Fig. 5(a)–(c), an increase in the anelasticity, endothermic tendency, and deviational decrease in the electrical resistivity can be observed, but the onset temperatures were somewhat different between the specimens or properties. Furthermore, the temperature changes in the anelasticity and endothermic tendency were rather gradual compared with the step-like changes of metallic glasses at the glass transition. The XRD patterns displayed in Fig. 1 indicate that the grain size and degree of the (111) preferred orientation are not identical among specimens A, B and C. The strong (111) preferred orientation suggests that the characteristics of the grain boundaries along or perpendicular to the thickness were different. It is known that the characteristics of the grain boundaries depend on the geometrical conditions14,46). It is surmised that the distribution of the grain boundary states leads to the broad temperature range where the characteristic changes were observed. The lower onset temperature of electrical resistivity compared with those of the anelasticity and endothermic tendency may reflect that the negative TCR of metallic glasses is observed even below the glass transition temperature.
The temperature range observed is much lower in n-Au than in the amorphous alloys; however, the transitional changes in anelasticity, thermal properties, and resistivity in Fig. 5 are qualitatively similar to the glass transition of the metallic glasses. It is noted that n-Au showed a creep deformation above 200 K under the applied stress of 80 MPa but no plastic deformation at 80 K under a few 100 MPa of stress22). This plastic deformation behavior is in good agreement with the assumption that the grain boundaries of n-Au are ideal elastic solids below ～130 K and the anelastic or viscoelastic nature becomes thermally activated above ～130 K22). It was reported that reversible first-order structural transformation in ∑5 grain boundaries of FCC metals was caused by temperature from molecular dynamics simulation13). The characteristic changes in anelastic, thermal, and electrical properties in Fig. 5 indicate that the transition in grain boundaries of n-Au is second-order like. We surmise that these characteristic changes reflect the glass-transition-like behavior of the grain boundaries in n-Au; in other words, the grain boundaries are in an amorphous state and different from those of p-metals.
For n-Au prepared by the gas deposition (GD) method, characteristic temperature changes were observed in the low-temperature anelastic, thermal, and electrical resistivity measurements below room temperature. In the anelastic measurement, the internal friction started to increase above ～180 K and a rapid increase linearly with temperature was observed above 200 K ($Q_{ > 200K}^{ - 1}$). Differential scanning calorimetry revealed that the heat flow of n-Au showed an endothermic tendency above ～170 K or a gradual increase in heat capacity. The increases in internal friction and endothermic tendency disappeared with the progression of the grain growth after annealing. The electrical resistivity of n-Au between 90 and 300 K was much higher than that of p-Au and showed a monotonous increase with temperature. However, the temperature coefficient of the resistivity of n-Au showed a deviation from a linear change and a slight upward convex curve above ～130 K. These characteristic temperature changes were similarly observed for the repetition of the cool-down and warm-up procedure below room temperature. It was reported that metallic glasses showed a step-like increase in the specific heat, a rapid increase in anelasticity, and a decrease in electrical resistivity at the glass transition temperature. The characteristic temperature changes of n-Au mentioned above are qualitatively similar to those of metallic glasses at the glass transition temperature. It indicates that the glass-transition-like change is thermally activated in the grain boundaries of n-Au.
The present study was financially supported by the JSPS KAKENHI Grant 25390027 from the Japan Society for the Promotion of Science (JSPS). The differential scanning calorimetry was carried out at the Chemical Analysis Division and the OPEN FACILITY, Research Facility Center for Science and Technology, University of Tsukuba. The authors thank Prof. Hiroshi Mizubayashi (University of Tsukuba) for valuable discussions.
